Abstract: The present invention relates to a method for determining hydrocarbon production for a reservoir. The method comprises determining a projector matrix based on a Jacobian matrix function of the gridded model, then splitting the Jacobian matrix into subsets of consecutive lines. For each subset of consecutive lines, creating a respective square matrix based on said subset. A determining eigenvectors and respective eigenvalues associated with the respective square matrix and then determining relevant eigenvectors having respective eigenvalues below a predetermined threshold. The projector is determined as a concatenation of the extended eigenvectors ordered according to multiple criteria: the respective order value of the subset; and the respective eigenvalue of the relevant eigenvector.

Abstract: A method for determining hydrocarbon production of a reservoir includes modeling the reservoir with a gridded model having a coarse partition and a fine partition. A first matrix is determined based on a Jacobian matrix function of the gridded model. A first projector matrix is determined as a concatenation of relevant generalized eigenvectors of a first square matrix and a second square matrix derived from the first matrix. A submatrix is extracted from the first projector matrix, and a projector matrix is determined based on a concatenation of vectors derived from relevant generalized eigenvectors of a third square matrix and a fourth square matrix derived from the submatrix. A preconditioner operator is determined based on the projector matrix, and hydrocarbon production is determined for the reservoir based on the preconditioner operator.

Abstract: The present invention relates to a method for determining hydrocarbon production for a reservoir. The method comprises determining a projector matrix based on a Jacobian matrix function of the gridded model, then splitting the Jacobian matrix into subsets of consecutive lines. For each subset of consecutive lines, creating a respective square matrix based on said subset. A determining eigenvectors and respective eigenvalues associated with the respective square matrix and then determining relevant eigenvectors having respective eigenvalues below a predetermined threshold. The projector is determined as a concatenation of the extended eigenvectors ordered according to multiple criteria: the respective order value of the subset; and the respective eigenvalue of the relevant eigenvector.